Problem: Rewrite as a simplified fraction. ${3.\overline{34} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 334.3434...\\ 1x &= 3.3434...\end{align*}}$ Subtracting the two equations, we have: ${99x = 331}$ ${x = \dfrac{331}{99}} \text{or} {3 \dfrac{34}{99}}$